Precoder structure for MIMO precoding

ABSTRACT

The teachings herein present a method and apparatus that implement and use a factorized precoder structure that is advantageous in terms of performance and efficiency. In particular, the teachings presented herein disclose an underlying precoder structure that allows for full PA utilization. According to this structure, an overall precoder is constructed from a conversion precoder and a tuning precoder. The conversion precoder comprises a block diagonal matrix and has 2┌k/2┐ columns, where k is a non-negative integer. Each tuning precoder has the following properties: all non-zero elements are constant modulus; every column has exactly two non-zero elements; and every row has exactly two non-zero elements; two columns either have non-zero elements in the same two rows or do not have any non-zero elements in the same rows; and two columns having non-zero elements in the same two rows are orthogonal to each other. If row m in a tuning precoder column has a non-zero element, so does row m+┌k/2┐.

RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.13/080,737 filed Apr. 6, 2011, which claims priority from the U.S.Provisional Patent Application No. 61/321,679 filed on Apr. 7, 2010.

FIELD OF THE INVENTION

The teachings herein generally relate to codebooks and precoding, andparticularly relate to a factorized precoder structure that provides forreuse of precoders across different transmit antenna configurations, andprovides for efficient precoder signaling.

BACKGROUND

Multi-antenna techniques can significantly increase the data rates andreliability of a wireless communication system. The performance is inparticular improved if both the transmitter and the receiver areequipped with multiple antennas, which results in a multiple-inputmultiple-output (MIMO) communication channel. Such systems and relatedtechniques are commonly referred to simply as MIMO.

The 3GPP LTE standard is currently evolving with enhanced MIMO support.A core component of this support in LTE is the support of MIMO antennadeployments and MIMO related techniques. A current working assumption inLTE-Advanced is the support of an 8-layer spatial multiplexing mode for8 transmit (Tx) antennas, with the possibility of channel dependentprecoding. The spatial multiplexing mode provides high data rates underfavorable channel conditions.

With spatial multiplexing, an information carrying symbol vector s ismultiplied by an N_(T)×r precoder matrix W_(N) _(T) _(×r), which servesto distribute the transmit energy in a subspace of the N_(T)(corresponding to N_(T) antenna ports) dimensional vector space. Theprecoder is typically selected from a codebook of possible precoders,and typically indicated by means of a precoder matrix indicator (PMI).The PMI value specifies a unique precoder in the codebook for a givennumber of symbol streams.

However, certain challenges arise in this context. For example,different antenna configurations can require precoder structures of onetype or another, which complicates the storage of predefined codebooksof precoders. Still further, the dynamic use of Single User (SU) MIMOand Multi-User (MU) MIMO modes complicates codebook design becauseprecoders that are optimal for SU-MIMO generally will not be optimal forMU-MIMO. As a further complication, the overhead associated withreporting precoder information, e.g., precoder recommendations, from areceiver to a transmitter may be problematic. This is true, for example,in the LTE downlink where the Physical Uplink Control Channel (PUCCH)cannot bear as large a payload size as the Physical Uplink SharedChannel (PUSCH).

SUMMARY

The teachings herein present a method and apparatus that implement anduse a factorized precoder structure that is advantageous in terms ofperformance and efficiency. In particular, the teachings presentedherein disclose an underlying precoder structure that allows for certaincodebook reuse across different transmission scenarios, including fortransmission from a single Uniform Linear Array (ULA) of transmitantennas and transmission from cross-polarized subgroups of suchantennas. According to the contemplated precoder structure, an overallprecoder is constructed from a conversion precoder and a tuningprecoder. The conversion precoder includes antenna-subgroup precoders ofsize N_(T)/2, where N_(T) represents the number of overall antenna portsconsidered. Correspondingly, the tuning precoder controls the offset ofbeam phases between the antenna-subgroup precoders, allowing theconversion precoder to be used with cross-polarized arrays of N_(T)/2antenna elements, and with co-polarized arrays of N_(T) antennaelements.

One embodiment disclosed herein relates to a wireless communicationtransceiver and an associated method, where another transceiver precodestransmissions to the transceiver based at least in part on receivingchannel state information from the transceiver. Here, the channel stateinformation includes precoder information for the other transmitter. Asan example case, the transceiver is a user equipment (UE) and the othertransceiver is a base station in a wireless communication networksupporting the UE, and the UE sends precoder information to the basestation that indicates precoder recommendations by the UE. As aparticular example, the base station is an eNodeB configured for MIMOoperation in an LTE network, and the UE is an LTE handset or other itemof communication equipment configured for MIMO operation in the LTEcontext.

The transceiver is configured to select entries from one or morecodebooks, where indications of the selected entries serves as theaforementioned precoder information sent to the other transceiver. Thetransceiver selects the entries as a selected conversion precoder and aselected tuning precoder, or as a selected overall precodercorresponding to a selected conversion precoder and a selected tuningprecoder. It will be understood that the selections may be made andreported dynamically, on a periodic or as needed basis, to reflectchanging channel conditions. The transceiver is further configured totransmit the indications of the selected entries in the channel stateinformation.

Several aspects of the above operations center on the stored codebook(s)and, in particular, the underlying structure of the conversion andtuning precoders (or corresponding overall precoders) stored in them.The one or more codebooks stored at the transceiver include entriescomprising a plurality of different conversion precoders and entriescomprising a number of corresponding tuning precoders, or includeentries comprising a plurality of overall precoders, with each overallprecoder comprising the product of a conversion precoder and a tuningprecoder.

In one embodiment, the codebook comprises N_(T)Q conversion precoders.Each conversion precoder comprises a block diagonal matrix in which ablock comprises an antenna-subgroup precoder. In turn, eachantenna-subgroup precoder is a matrix block with N_(T)/2 rows andbelongs to a set of N_(T)Q different DFT-based beams, where Q is aninteger equal to or greater than 2, and where each said tuning precoderincludes a phase shift element taken from a 2Q Phase Shift Keying (PSK)alphabet and provides at least 2Q relative phase shifts for offsettingbeam phases between the antenna-subgroup precoders in a correspondingone of the conversion precoders. Thus, each overall precoder comprises aDFT-based precoder providing for N_(T) transmit beams across the N_(T)transmit antenna ports.

This advantageous precoder structure allows, for example, precoding fromcross-polarized subgroups of antennas, where the set of beams from eachsubgroup is controlled by a corresponding one of the DFT-basedantenna-subgroup precoders in the conversion precoder selected by thetransceiver performing the precoded transmission. Further, that sameprecoder structure allows for beamforming across an equal-sized overallarray of antennas, where the beam-phase offsets between subgroups isprovided by the correspondingly selected tuning precoder.

In other embodiments, each conversion precoder comprises a blockdiagonal matrix and has 2┌k/2┐ columns, where k is a non-negativeinteger. Each tuning precoder has the following properties: all non-zeroelements are constant modulus; every column has exactly two non-zeroelements; and every row has exactly two non-zero elements; two columnseither have non-zero elements in the same two rows or do not have anynon-zero elements in the same rows; and two columns having non-zeroelements in the same two rows are orthogonal to each other. If row m ina tuning precoder column has a non-zero element, so does row m+┌k/2┐.This precoder structure allows for full PA utilization.

Still further, this arrangement in one or more embodiments is exploitedby reporting conversion precoder selections at a time or frequencyresolution lower than that used for reporting tuning precoderselections. As one example, the transceiver sends indications of theselected tuning precoder more frequently than it sends indications ofthe selected conversion precoder. The other transceiver is configured todetermine the selected overall precoder in between receiving conversionprecoder selections, based on keeping the same conversion precoder butupdating the overall precoder calculation with each newly receivedtuning precoder selection. The transceiver also may send one conversionprecoder selection to be used in common with two or more tuning precoderselections, each one representing a different sub-band of a frequencyband associated with the common conversion precoder.

In another embodiment, a method and associated transceiver are directedto precoding multi-antenna transmissions to another wirelesscommunication transceiver. This embodiment can be understood relating tothe transmitter side of the disclosed teachings, while the precedingexamples related to the receiver side. Thus, in this example, thetransceiver, which may be a base station precoding to a targeted UE,receives channel state information from the other transceiver, wherethat information includes precoder information, such as indications ofprecoder selections representing precoder recommendations.

The transceiver is configured to use the received precoder informationto identify the precoder recommendations from the other transceiver. Inthe case where the received precoder information includes selectionindicators such as PMIs or other codebook index values, the transceiveruses the selection indicators to select entries from one or morecodebooks. The transceiver is further configured to precode atransmission to the other transceiver, based at least in part on theprecoder recommendations. In this regard, it will be understood that thetransceiver may simply follow the precoder recommendations sent by theother transceiver. However, the transceiver does not necessarily use theprecoder selections indicated by the other transceiver and instead maymake different selections, based on overall circumstances, such as thescheduling of multiple such transmissions, the MIMO mode in use, etc.

Of particular, interest, the transceiver uses the same one or morecodebooks used by the other transmitter when making precoderrecommendations. For example, both transceivers store copies of the samecodebooks, or one of them stores one or more codebooks that areequivalent to those stored at the other transceiver.

As such, the transceiver's codebook(s), which may be held in a memory ofthe transceiver, store entries comprising a plurality of differentconversion precoders and entries comprising a number of correspondingtuning precoders, or entries comprising a plurality of overallprecoders, where each overall precoder comprises the product of aconversion precoder and a tuning precoder. In one embodiment, thecodebook(s) comprise N_(T)Q different conversion precoders. Eachconversion precoder out of the N_(T)Q different entries for theconversion precoders comprises a block diagonal matrix, in which eachblock comprises a DFT-based antenna-subgroup precoder that correspondsto a subgroup of N_(T) transmit antenna ports. Each suchantenna-subgroup precoder provides N_(T)Q different DFT based beams forthe corresponding subgroup, where Q is an integer value and where theN_(T)Q different conversion precoders, together with one or more of thetuning precoders, correspond to a set of N_(T)Q different overallprecoders. Each overall precoder in that set represents a size-N_(T)DFT-based beam over the N_(T) transmit antennas ports.

In other embodiments, each conversion precoder comprises a blockdiagonal matrix and has 2┌k/2┐ columns, where k is a non-negativeinteger. Each tuning precoder has the following properties: all non-zeroelements are constant modulus; every column has exactly two non-zeroelements; and every row has exactly two non-zero elements; two columnseither have non-zero elements in the same two rows or do not have anynon-zero elements in the same rows; and two columns having non-zeroelements in the same two rows are orthogonal to each other. If row m ina tuning precoder column has a non-zero element, so does row m+┌k/2┐.

The transceiver in one or more embodiments is a base station configuredfor operation in a wireless communication network, e.g., an eNodeBconfigured for operation in an LTE network. In this case, the basestation operates as a multi-antenna MIMO transmitter that considersprecoder recommendations from the other transceiver, which may be a UEor other wireless communication device that is supported by the basestation.

Of course, the above brief summary of features and advantages is notlimiting. Other features and advantages will be apparent from thefollowing detailed description of example embodiments and from theaccompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of example embodiments of a first transceiverthat is configured to transmit precoded transmissions to a secondtransceiver that is configured to provide precoder recommendations tothe first transceiver.

FIG. 2 is a diagram of one embodiment of a conversion precoder having ablock-diagonal structure and including two antenna-subgroup precoders.

FIG. 3 is a block diagram of an example wireless communication network,where the first transceiver of FIG. 1 is represented as a network basestation and the second transceiver of FIG. 1 is represented as an itemof user equipment.

FIG. 4 is a diagram of example conversion and tuning precoders, as usedto form an overall precoder.

FIGS. 5 and 6 are diagrams of example codebooks, where FIG. 5 depictsone codebook containing conversion precoders and another one containingtuning precoders, and where FIG. 6 depicts one codebook containingoverall precoders, each corresponding to a particular conversionprecoder and a particular tuning precoder.

FIG. 7 is a logic flow diagram of one embodiment of a method ofproviding precoder recommendations from a second transceiver to a firsttransceiver, such as is shown in FIG. 1.

FIG. 8 is a partial block diagram of one embodiment of processingcircuitry in the second transceiver, for determining precoderrecommendations.

FIG. 9 is a logic flow diagram of one embodiment of a method ofprecoding transmissions from a first transceiver to a secondtransceiver, such as are shown in FIG. 1.

FIG. 10 is a partial block diagram of one embodiment of processingcircuitry within the first transceiver for controlling the precoding oftransmissions to the second transceiver.

FIG. 11 is a block diagram of one embodiment of further precodingcircuits for the first transceiver.

DETAILED DESCRIPTION

FIG. 1 depicts a first wireless communication transceiver 10 and asecond wireless communication transceiver 12, referred to forconvenience as transceivers 10 and 12. The transceiver 10 includes anumber of antennas 14 and associated transceiver circuits 16, includingone or more radiofrequency transmitters 18 and receivers 20. Stillfurther, the transceiver 10 includes control and processing circuits 22,which include a feedback processor 24, a precoding controller 26, andone or more memory/storage devices 28 that store one or more codebooks30. The memory/storage devices 28 are simply referred to as “memory 28”for convenience.

The one or more codebooks 30 stored at the transceiver 10 includeentries comprising N_(T) Q different conversion precoders 32 and entriescomprising a number of corresponding tuning precoders 34, or includeentries comprising a plurality of overall precoders 36, with eachoverall precoder 36 comprising the product of a conversion precoder 32and a tuning precoder 34. Here, it will be understood that the referencenumber “32” is used to refer to conversion precoders in the plural andsingular senses, but each conversion precoder 32 generally is uniquefrom the others, in terms of the numeric values representing its matrixelements. The same understanding applies to the reference numbers “34”and “36” as used for the tuning precoders and overall precoders,respectively.

Each conversion precoder 32 comprises a block diagonal matrix in whicheach block comprises a DFT-based antenna-subgroup precoder 38 (shown inFIG. 2). Each antenna-subgroup precoder 38 is a matrix block withN_(T)/2 rows and belongs to a set of N_(T)Q different DFT-based beams,where Q is an integer equal to or greater than 2, and where each tuningprecoder 34 includes a phase shift element taken from a 2Q Phase ShiftKeying (PSK) alphabet and provides at least 2Q relative phase shifts foroffsetting beam phases between the antenna-subgroup precoders 38 in acorresponding one of the conversion precoders 32.

Continuing with FIG. 1, the second transceiver 12 includes a number ofantennas 40 and associated transceiver circuits 42 (including one ormore radio frequency receivers 44 and transmitters 46). The transceiver12 further includes control and processing circuits 48. At leastfunctionally, the control and processing circuits 48 include receivedsignal processing circuitry 50, e.g., demodulation/decoding circuits,one or more estimation circuits 52 for estimating channel conditionsand/or signal quality, a precoding feedback generator 54, and one ormore memory/storage devices 56 (e.g., non-volatile memory such as EEPROMor FLASH, simply referred to as “memory 56” for convenience).

Memory 28 at the transceiver 10 and memory 56 at the transceiver 12 eachstore a copy of the same one or more codebook(s) 30, or equivalently,they store codebook(s) or equivalent information that allow thetransceiver 10 and the transceiver 12 to have the same understanding interms of the precoders selected by the transceiver 12 as “precoderrecommendations.” That is, in operation the transceiver 10 precodestransmissions 60 to the transceiver 12 based on determining a precoderoperation to apply—i.e., based on determining the particular MIMOconfiguration and corresponding precoder weights to be used formulti-antenna transmission from the transceiver 10 to the transceiver12.

The transceiver 10 determines the precoder operation based at least inpart on receiving channel state information (CSI) 62 from thetransceiver 12, which includes precoder information 64. The precoderinformation 64 may be understood as providing recommendations forprecoder selection, and the precoder information 64 thus may be providedas Precoder Matrix Indicator (PMI) values for indexing into the one ormore codebooks 30, or as some other type of selection indicators. In oneor more embodiments, the transceiver 10 sends control signaling 66 tothe transceiver 12, to control its precoder information 64. For example,the control signaling 66 may restrict precoder selections to aparticular subset of precoders—e.g., those intended for SU-MIMO mode, orthose intended for MU-MIMO mode.

In at least one embodiment, the control and processing circuits 22 ofthe transceiver 10 at least in part comprise computer-based circuitry,e.g., one or more microprocessors and/or digital signals processors, orother digital processing circuitry. In at least one embodiment, suchcircuitry is specially configured to implement the methods taught hereinfor the transceiver 10, based on executing stored computer programinstructions. These instructions are, in one or more embodiments, storedin the memory 28. Likewise, in at least one embodiment, the control andprocessing circuits 48 of the transceiver 12 are implemented at least inpart via programmable digital processing circuitry. For example, thecontrol and processing circuits 48 in one or more embodiments includeone or more microprocessors or digital signal processors configured toimplement at least a portion of the method taught herein for thetransceiver 12, based on executing computer program instructions storedin the memory 56.

Such implementations may be understood in the example case of FIG. 3where the transceiver 10 is configured as a wireless communicationnetwork base station 70 operating in a wireless communication network72. The transceiver 12 is configured as a UE 74 and is supported by thenetwork 72. The simplified network diagram further depicts a RadioAccess Network (RAN) 76, including one or more the base stations 70, andan associated Core Network (CN) 78. This arrangement communicativelycouples the UE 74 to other devices in the same network and/or in one ormore other networks. To this end, the CN 78 is communicatively coupledto one or more external networks 80, such as the Internet and/or thePSTN.

The base station 70 stores the one or more codebooks 30, as does the UE74. Accordingly, one sees precoded transmissions 60 sent from the basestation 70 to the UE 74, along with optional control signaling 66 thatcontrols the precoder recommendations made by the UE 74. Such signalingmay be sent using Radio Resource Control (RRC) signaling, for example.

One also sees the transmission of precoder information 64 (i.e.,precoder selection feedback) from the UE 74 to the base station 70. Asnoted, these recommendations comprise selection indicators, such asPMIs, that indicate the particular conversion and tuning precoders 32and 34 that are currently recommended by the UE 74 for use by the basestation 70 in precoding transmissions to the UE 74. In anotherembodiment, the recommendations comprise indications of the selectedoverall precoder 36, which corresponds to the selection of a particularconversion precoder 32 and a particular tuning precoder 34. However,even in this embodiment, an indication of the recommended overallprecoder 36 can be understood as being equivalent to the indication ofrecommend conversion and tuning precoders 32 and 34.

FIG. 4 provides a better illustration of this “factorized precoder”flexibility, where an overall precoder 36 (denoted as “W”) is formed asthe matrix multiplication of a selected conversion precoder 32 (denotedas “W^((c))”) and a selected tuning precoder 34 (denoted as “W^((t))”).The codebook(s) 30 can comprise one codebook that includes a number ofconversion precoders 32 at first index positions and a number of tuningprecoders 32 at second index positions, thus allowing different rangesof index values for denoting conversion precoder selections and tuningprecoder selections. Alternatively, the codebook(s) 30 can beimplemented as two codebooks, such as shown in FIG. 5. Here, onecodebook 82 contains conversion precoders 32, and one codebook 84contains tuning precoders 34. As a further alternative, FIG. 6illustrates that the one or more codebooks 30 may comprise one codebook86 that contains a set of overall precoders 36, with each overallprecoder 36 formed as the product (matrix multiplication) of aparticular conversion precoder 32 and a particular tuning precoder 34.

In the case where separate conversion and tuning precoder codebooks 82and 84 are used, the precoder information 64 may comprise a first indexvalue that indexes (points) to particular conversion precoder 32 in thecodebook 82, and a second index value that indexes (points) to aparticular tuning precoder 34 in the codebook 84. In the case where onecodebook 86 of overall precoders 36 is used, the index values may betwo-dimensional row-column index values that point to a particularoverall precoder 36 in a table structure.

Advantageously, in any of these cases, the precoder information 64 mayinclude separate indications for conversion and tuning precoderselections. This provides for advantageous gains in signalingefficiency. For example, the transceiver 12 sends conversion precoderrecommendations on a first interval, and tuning precoder recommendationson a second, shorter interval. In this case, from the perspective of thetransceiver 10, the overall precoder 36 as recommended by thetransceiver 12 is the product of the most recently recommendedconversion precoder 32 and the most recently recommended tuning precoder34. In another example embodiment, the transceiver 12 recommends oneconversion precoder 32 for an overall frequency band, and recommends twoor more tuning precoders 34 for each of two or more sub-bands. Thetransceiver 10 in this case recognizes the precoder information 64 astwo or more overall precoders 36, each formed from the common conversionprecoder 32 and a respective one of the two or more recommended tuningprecoders 34.

In the case where a single codebook 86 of overall precoders 36 is used,that codebook may be arranged such that each row (or column) correspondsto a particular conversion precoder 32, while each column (or row)corresponds to a particular tuning precoder 34. A complete index thuscomprises a row pointer and a column pointer, and the transceiver 12 cansend these together or separately. For example, row pointer updates canbe sent on one time interval or for an overall frequency band, for theconversion precoder selection, while column pointer updates can be senton another faster time interval, or for particular sub-bands of theoverall frequency band, for the tuning precoder selection(s). In thisregard, it should be understood that one conversion precoder 32 can beused as a common base for two or more overall precoders 36, based onmultiplying it with each of two or more tuning precoders 34.

With these examples in mind, FIG. 7 illustrates a method 700 implementedin the transceiver 12. The transceiver 12 is configured to carry out themethod 700 based on executing computer program instructions stored inits memory 56 and/or or based on having specifically configuredcircuitry. In any case, the method 700 includes the transceiver 12selecting entries from one or more codebooks 30 as a selected conversionprecoder 32 and a selected tuning precoder 34, or as a selected overallprecoder 36 corresponding to a selected conversion precoder 32 and aselected tuning precoder 34 (Block 702). It will be understood that theprecoding feedback generator 54 is adapted to perform these selections,based on computing the recommendations according to the factorizedconversion and tuning precoder format.

Further, it will be understood that the transceiver 12 stores thecodebook(s) 30 in its memory 56—e.g., it stores one codebook 82 ofconversion precoders 32 and another codebook 84 of tuning precoders 34,or it stores a codebook 86 of overall precoders 36, e.g., with eachrepresenting the combination of a particular conversion precoder 32 anda particular tuning precoder 34. With that in mind, the method 700continues with transmitting precoder information 64 to the transceiver10 (Block 704).

As noted, separate indications for the selected conversion precoder 32and the selected tuning precoder 34 may be used, to allow more frequentor higher resolution signaling of the tuning precoder recommendationsand slower or lower (frequency) resolution signaling of the conversionprecoder recommendations. In at least one embodiment, tuning precoderrecommendations are sent on a lower layer of the signaling protocol usedfor communicatively coupling the transceiver 12 to the transceiver 10than is used for signaling the conversion precoder recommendations. Forexample, referring to the wireless network case of FIG. 3, theconversion precoder recommendations are sent using Radio ResourceControl (RRC) signaling, while the tuning precoder recommendations aresent on a lower layer.

Regardless, the transceiver 12 makes its precoding recommendationselections based on, for example, evaluating channel conditions via theestimation circuits 52, which estimate channel conditions and/orevaluate received signal quality, such as SNR. And, as noted, it maycontrol its recommendations responsive to control signaling 66 receivedfrom the transceiver 10. Such an arrangement is seen in the example ofFIG. 8, wherein the precoding feedback generator 54 (abbreviated as“PFG” in the illustration) performs dynamic selection of conversionprecoders 32 and tuning precoders 34 from the codebook(s) 30, based onevaluating the channel properties as determined by the estimationcircuits 52.

It will be understood that the channel property information comprises,for example, complex coefficients representing multi-path propagationchannel characteristics and/or channel properties such as impairmentcorrelations, etc. The precoder selections may be made subject to anyrestrictions imposed by the control signaling 66, which may restrict therecommendation selections to predefined subsets of the precoders, suchas one subset for the case where the transceiver 10 is operating in anMU-MIMO mode, and another subset for case where the transceiver 10 isoperating in a SU-MIMO mode. This example is particularly pertinent tothe example network case of FIG. 3, where the transceiver 10 is a basestation 70 and may support pluralities of UEs 74 (“users”).

While FIG. 7 illustrates what might be considered as an example of the“receive” side method, FIG. 9 illustrates an example case for the“transmit” side method—i.e., it details example operations implementedby the transceiver 10. The method 900 is directed to precodingmulti-antenna transmissions 60 to the transceiver 12, and includesreceiving channel state information 62 from the other transceiver 12,including receiving selection indicators as the precoder information 64(Block 902). The method 900 continues with identifying the precoderinformation 64 by selecting entries from one or more codebooks 30 storedat the transceiver 10, based on the selection indications included inthe channel state information 62 (Block 904). Here, it will beunderstood that the feedback processor 24 at the transceiver 10 isadapted to handle the factorized feedback contemplated for the precoderinformation 64. That is, the feedback processor 24 is configured toextract and provide the conversion and tuning precoder recommendationsincluded in the channel state information 62.

The method 900 further includes the transceiver 10 precoding atransmission 60 to the transceiver 12, based at least in part on theprecoder information 64 (Block 906). As noted, the “selection” performedin Block 904 can be understood as the transceiver 10 identifying theoverall precoder 36 that the transceiver 12 recommends for precoding thetransmission 60 to the transceiver 12. However, when the transceiver 10determines the actual precoding operation to apply in generating thetransmission 60, it may follow the recommendations or make its ownselections or modifications.

FIG. 10 illustrates an example configuration where the feedbackprocessor 24 and precoding controller 26 (abbreviated “FP” and “PC”)determine the actual precoder selections to be used for precoding thetransmissions 60 to the transceiver 12. These decisions depend on, forexample, the precoder information 64 and channel properties as indicatedin the channel state information 62, and on scheduling information. Inparticular, in the case where the transceiver 10 transmits to multipletransceivers 12, it may consider plural sets of data (e.g., channelconditions and scheduling data for multiple transceivers 12) indetermining its precoding operations.

As for generating the precoded transmission 60, FIG. 11 depicts aprecoding circuit 90 included in the transmitter 18 of the transceiver10 and it will be understood as being associated with the precodingcontroller 26. The precoding circuit 90 enables the transceiver 10 toprecode transmissions according to an applied precoding operation, andthe transceiver 10 may have more than one such circuit.

According to the example illustration, the precoding circuit 90 receivesinput data, e.g., information symbols to be transmitted, and it includeslayer processing circuits 92 that are responsive to a rank controlsignal from the precoding controller 26. Depending on the transmit rankin use, the input data is placed onto one or more spatial multiplexinglayers and the corresponding symbol vector(s) s are input to a precoder94.

As an example, the precoder 94 is shown as applying a selected overallprecoder 36 (denoted as “W”) that is formed as the matrix multiplicationof a selected conversion precoder 32 (denoted as “W^((c))”) and aselected tuning precoder 34 (denoted as “W^((t))”). More broadly, theprecoder 94 applies a precoding operation determined by the precodingvalue(s) provided to it by the precoding controller 26. Those values mayor may not follow the precoder information 64 included in the channelstate information 62 received from the transceiver 12, but thetransceiver 10 at least considers those recommendations in its precodingdeterminations. In any case, the precoder 94 outputs precoded signals toInverse Fast Fourier Transform (IFFT) processing circuits 96, which inturn provide signals to a number of antenna ports 98 associated with theantennas 14 shown in FIG. 1.

Note that these ports are managed as a ULA in one embodiment, and aremanaged as antenna subgroups in another embodiment. Advantageously, thesame conversion precoders 32 can be used for either case because eachconversion precoder 32 comprises a block diagonal matrix.

In more detail, each conversion precoder 32 is one out of N_(T)Qdifferent entries in a codebook. Each conversion precoder 32 comprises ablock diagonal matrix. Each such block diagonal matrix is a DFT-basedantenna-subgroup precoder 38 that corresponds to a subgroup of N_(T)transmit antenna ports 98 and provides N_(T)Q different DFT based beamsfor the corresponding subgroup, where Q is an integer value and wherethe N_(T)Q different conversion precoders 32, together with one or moreof the tuning precoders 34, correspond to a set of N_(T)Q differentoverall precoders 36, each overall precoder 36 thus representing asize-N_(T) DFT-based beam over the N_(T) transmit antennas ports 98.

To better understand the above arrangement, consider thatantenna-subgroup precoder 38 is a matrix block with N_(T)/2 rows andbelongs to a set of N_(T)Q different DFT-based beams, where Q is aninteger equal to or greater than 2. Further, each tuning precoder 34includes a phase shift element taken from a 2Q Phase Shift Keying (PSK)alphabet and provides at least 2Q relative phase shifts for offsettingbeam phases between the antenna-subgroup precoders 38 in a correspondingone of the conversion precoders 32. With this structure, each overallprecoder 36 comprises a DFT-based precoder providing for N_(T) transmitbeams across N_(T) transmit antenna ports.

As such, in at least one embodiment, the transceiver 10 is configured toperform DFT-based precoding of transmissions 60 from two or moresubgroups of the antennas 14 at the transceiver 10. These operations arebased on the transceiver 10 using the antenna-subgroup precoders 38 inone of the conversion precoders 32, as selected by the transceiver 10from the one or more codebooks 30 based at least in part on the precoderinformation 64.

To better understand the advantages of the above precoder structure andin development of the underlying mathematical operations, consider ageneral precoder matrix. If the precoder matrix is confined to haveorthonormal columns, then the design of the codebook of precodermatrices corresponds to a Grassmannian subspace packing problem. In anycase, the r symbols in the symbol vector s each correspond to a layerand r is referred to as the transmission rank. In this way, spatialmultiplexing is achieved because multiple symbols can be transmittedsimultaneously over the same time/frequency resource element (TFRE). Thenumber of symbols r is typically adapted to suit the current propagationchannel properties.

LTE uses OFDM in the downlink (and DFT precoded OFDM in the uplink) andhence the received N_(R)×1 vector y_(n) for a certain TFRE on subcarriern (or alternatively data TFRE number n) is thus modeled byy _(n) =H _(n) W _(N) _(T) _(×r) s _(n) +e _(n)  (1)where e_(n) is a noise/interference vector obtained as realizations of arandom process and H_(n) is the complex channel. The precoder, W_(N)_(T) _(×r), can be a wideband precoder, which is constant overfrequency, or frequency selective.

Conventionally, the precoder matrix is often chosen to match thecharacteristics of the N_(R)×N_(T) MIMO channel matrix H, resulting inso-called channel dependent precoding. This is also commonly referred toas closed-loop precoding and essentially tries to focus the transmitenergy into a subspace which is strong in the sense of conveying much ofthe transmitted energy to the targeted receiver. In addition, theprecoder matrix also may be selected with the goal of orthogonalizingthe channel, meaning that after proper linear equalization at a UE orother targeted receiver, the inter-layer interference is reduced.

According to the factorized precoder structure disclosed herein, theconversion precoders 32 are configured to have dimension N_(T)×k, wherek is configurable and preferably is less than the number of transmitantenna ports N_(T) considered for precoding. In this regard k<N_(T)advantageously restricts the number of channel dimensions that must beaccounted for in the tuning precoders 34. Correspondingly, the tuningprecoders 34 are configured to have dimension k×r, where r is thetransmission rank. This arrangement is shown below:W _(N) _(T) _(×r) =W _(N) _(T) _(×k) ^((c)) W _(k×r) ^((t)),  (2)where the conversion precoder 32, W_(N) _(T) _(×k) ^((c)), strives forcapturing wideband/long-term properties of the channel such ascorrelation, while the tuning precoder 34, W_(k×r) ^((t)), targetsfrequency-selective/short-term properties of the channel.

The conversion precoder 32 exploits the correlation properties forfocusing the tuning precoder 34 in “directions” where the propagationchannel H on average is “strong.” Typically, this is accomplished byreducing the number of dimensions k covered by the tuning precoder 34.In other words, the conversion precoder 32 becomes a tall matrix with areduced number of columns. Consequently, the number of rows k of thetuning precoder 34 is reduced as well. With such a reduced number ofdimensions, the codebook used for storing the tuning precoders 34 can bemade smaller, while still maintaining good performance.

In one arrangement already shown, the conversion precoders 32 are in onecodebook 82 and the tuning precoders 34 are in another codebook 84. Thisarrangement exploits the fact that the conversion precoders 32 shouldhave high spatial resolution and thus are advantageously implemented asa codebook 82 with many elements, while the codebook 84 for the tuningprecoders 34 should be made small to keep the signaling overhead at areasonable level.

To see how correlation properties are exploited and dimension reductionachieved, consider the case where the N_(T) different antennas 14 at thetransceiver 10 are arranged into N_(T)/2 closely spaced cross-poles.Based on the polarization direction of the antenna subsets, the antennasin the closely spaced cross-pole setup can be divided into two groups,where each group is a closely spaced co-polarized Uniform Linear Array(ULA) with N_(T)/2 antennas. Closely spaced antennas often lead to highchannel correlation and the correlation can in turn be exploited tomaintain low signalling overhead. The channels corresponding to eachsuch antenna group ULA are denoted H_(/) and H_(\), respectively.

For convenience in notation, the following equations drop the subscriptsindicating the dimensions of the matrices as well as the subscript n.Assume that each conversion precoder 32 has a block diagonal structure,

$\begin{matrix}{W^{(c)} = {\begin{bmatrix}{\overset{\sim}{W}}^{(c)} & 0 \\0 & {\overset{\sim}{W}}^{(c)}\end{bmatrix}.}} & (3)\end{matrix}$The product of the MIMO channel H and the overall precoder 36 can thenbe written as

$\begin{matrix}\begin{matrix}{{HW} = {\left\lbrack {H_{/}\mspace{14mu} H_{\smallsetminus}} \right\rbrack W^{(c)}W^{(t)}}} \\{= {{\left\lbrack {H_{/}\mspace{14mu} H_{\smallsetminus}} \right\rbrack\begin{bmatrix}{\overset{\sim}{W}}^{(c)} & 0 \\0 & {\overset{\sim}{W}}^{(c)}\end{bmatrix}}W^{(t)}}} \\{= {{\left\lbrack {H_{/}{\overset{\sim}{W}}^{(c)}\mspace{14mu} H_{\backslash}{\overset{\sim}{W}}^{(c)}} \right\rbrack W^{(t)}} = {H_{eff}{W^{(t)}.}}}}\end{matrix} & (4)\end{matrix}$As seen, the matrix {tilde over (W)}^((c)) separately precodes eachantenna group ULA, thereby forming a smaller and improved effectivechannel H_(eff). As such, the blocks within W^((c)) are referred to asantenna subgroup precoders 38. If {tilde over (w)}^((c)) corresponds toa beamforming vector, the effective channel would reduce to having onlytwo virtual antennas, which reduces the needed size of the codebook(s)30 used for the second tuning precoder matrix W^((t)) when tracking theinstantaneous channel properties. In this case, instantaneous channelproperties are to a large extent dependent upon the relative phaserelation between the two orthogonal polarizations.

It is also helpful for a fuller understanding of this disclosure toconsider the theory regarding a “grid of beams,” along with DiscreteFourier Transform (DFT) based precoding. DFT based precoder vectors forN_(T) transmit antennas can be written in the form

$\begin{matrix}{\mspace{79mu}{{w_{n}^{({N_{T},Q})} = \left\lbrack {w_{1,n}^{({N_{T},Q})}\mspace{14mu} w_{2,n}^{({N_{T},Q})}\mspace{14mu}\ldots\mspace{14mu} w_{N_{T},n}^{({N_{T},Q})}} \right\rbrack^{T}}{{w_{m,n}^{({N_{T},Q})} = {\exp\left( {j\;\frac{2\pi}{N_{T}Q}{mn}} \right)}},{\quad{{m = 0},\ldots\mspace{14mu},{N_{T} - 1},{n = 0},\ldots\mspace{14mu},{{Q\; N_{T}} - 1},}}}}} & (5)\end{matrix}$where w_(m,n) ^((N) ^(T) ^(,Q)) is the phase of the m:th antenna, n isthe precoder vector index (i.e., which beam out of the QN_(T) beams) andQ is the oversampling factor. As seen, the phase increases with the sameamount from one antenna port to another, i.e., linearly growing phasewith respect to the antenna port index m. This is in fact acharacteristic of DFT-based precoding. Thus DFT based precoder vectorsmay include additional phase shifts on top of those shown in the aboveexpression as long as the overall phase shift is increasing linearlywith m.

For good performance, it is important that the array gain function oftwo consecutive transmit beams overlaps in the angular domain, so thatthe gain does not drop too much when going from one beam to another.This requires an oversampling factor of at least Q=2. Thus for N_(T)antennas, at least 2N_(T) beams are needed.

An alternative parameterization of the above DFT based precoder vectorsis

$\begin{matrix}{w_{l,q}^{({N_{T},Q})} = \left\lbrack {{{\begin{matrix}w_{1,{{Q\; l} + q}}^{({N_{T},Q})} & \begin{matrix}w_{2,{{Q\; l} + q}}^{({N_{T},Q})} & \ldots & \left. w_{N_{T},{{Q\; l} + q}}^{({N_{T},Q})} \right\rbrack^{T}\end{matrix}\end{matrix}w_{m,{{Q\; l} + q}}^{({N_{T},Q})}} = {\exp\left( {j\;\frac{2\pi}{N_{T}}{m\left( {l + \frac{q}{Q}} \right)}} \right)}},} \right.} & (6)\end{matrix}$for m=0, . . . , N_(T)−1, l=0, . . . , N_(T)−1, q=0, 1, . . . , Q−1, andwhere l and q together determine the precoder vector index via therelation n=Ql+q. This parameterization also highlights that there are Qgroups of beams, where the beams within each group are orthogonal toeach other. The q:th group can be represented by the generator matrix

$\begin{matrix}{G_{q}^{(N_{T})} = \left\lbrack \begin{matrix}w_{0,q}^{({N_{T},Q})} & \begin{matrix}w_{1,q}^{({N_{T},Q})} & \ldots & {\left. w_{{N_{T} - 1},q}^{({N_{T},Q})} \right\rbrack.}\end{matrix}\end{matrix} \right.} & (7)\end{matrix}$By insuring that only precoder vectors from the same generator matrixare being used together as columns in the same precoder, it isstraightforward to form sets of precoder vectors for use in so-calledunitary precoding where the columns within a precoder matrix should forman orthonormal set.

Further, to maximize the performance of DFT based precoding, it isuseful to center the grid of beams symmetrically around the broad sizeof the array. Such a rotation of the beams can be done by multiplyingfrom the left the above DFT vectors w_(n) ^((N) ^(T) ^(,Q)) with adiagonal matrix W_(rot) having elements

$\begin{matrix}{\left\lbrack W_{rot} \right\rbrack_{mm} = {{\exp\left( {j\;\frac{\pi}{{QN}_{T}}m} \right)}.}} & (8)\end{matrix}$The rotation can either be included in the precoder codebook oralternatively can be carried out as a separate step where all signalsare rotated in the same manner and the rotation can thus be absorbedinto the channel from the perspective of the receiver (transparent tothe receiver). For the remainder of DFT-precoding discussion herein, itis tacitly assumed that rotation may or may not have been carried out aspart of DFT-based precoding.

One aspect of the above-described factorized precoder structure relatesto lowering the overhead associated with signaling the conversion andtuning precoders 32 and 34, based on signaling them with differentfrequency and/or time granularity. The use of a block diagonalconversion precoder 32 is specifically optimized for the case of atransmit antenna array comprising closely spaced cross-poles, but otherantenna arrangements exist as well. In particular, efficient performancewith a ULA of closely spaced co-poles should also be achieved using thesame conversion precoders 32. The precoder structures disclosed hereinadvantageously provide for use of the same conversion precoderstructure, irrespective of whether the transceiver 10 uses its antennasas a ULA of N_(T) closely-spaced co-poles, or as two subsetscross-poles, each subset having N_(T)/2 antenna elements.

In particular, in one or more embodiments, the conversion precoders 32comprise DFT-based precoders which are suitable for the two N_(T)/2element antenna group ULAs in a closely spaced cross-pole setup, whilestill providing for their re-use in forming the needed number of DFTbased size N_(T) precoders for an N_(T) element ULA. Moreover, one ormore embodiments disclosed herein provide a structure for the conversionprecoder that allows re-using existing codebooks with DFT basedprecoders and extending their spatial resolution.

In any case, an example embodiment illustrates re-using DFT basedprecoder elements for an antenna group ULA in a closely spacedcross-pole and also in creating a grid of beams with sufficient overlapfor a ULA of twice the number of elements compared with the antennagroup ULA. In other words, the conversion precoders 32 can be designedfor use with the multiple antennas 14 of the transceiver 10, regardlessof whether those antennas 14 are configured and operated as an overallULA of N_(T) antennas, or as two cross-polarized ULA subgroups, eachhaving N_(T)/2 antennas.

Consider again the block diagonal factorized precoder design given as

$\begin{matrix}{{W = {{W^{(c)}W^{(t)}} = {\begin{bmatrix}{\overset{\sim}{W}}^{(c)} & 0 \\0 & {\overset{\sim}{W}}^{(c)}\end{bmatrix}W^{(t)}}}},} & (9)\end{matrix}$and note that in order to tailor the transmission to ±45 degreescross-poles, the structure of a conversion precoder 32 can be modifiedby means of a multiplication from the left with a matrix

$\begin{matrix}{\begin{bmatrix}I & {I\;{\mathbb{e}}^{j\;\phi}} \\I & {{- I}\;{\mathbb{e}}^{j\;\phi}}\end{bmatrix},} & (10)\end{matrix}$which, for φ=0, rotates the polarizations 45 degrees to align withhorizontal and vertical polarization. Other values of φ may be used toachieve various forms of circular polarization.

For an N_(T) element ULA, the overall precoder 36 for rank 1 is to be anN_(T)×1 vector as

$\begin{matrix}{W = {w_{n}^{({N_{T},Q})} = \left\lbrack \begin{matrix}w_{1,n}^{({N_{T},Q})} & \begin{matrix}w_{2,n}^{({N_{T},Q})} & \ldots & {\left. w_{N_{T},n}^{({N_{T},Q})} \right\rbrack^{T}.}\end{matrix}\end{matrix} \right.}} & (11)\end{matrix}$For antennas m=0, 1, . . . , N_(T)/2−1,

$\begin{matrix}{{w_{m,n}^{({N_{T},Q})} = {{\exp\left( {j\;\frac{2\pi}{N_{T}Q}{mn}} \right)} = {{\exp\left( {j\frac{2\pi}{\frac{N_{T}}{2}\left( {2Q} \right)}{mn}} \right)} = w_{m,n}^{({{N_{T}/2},{2Q}})}}}},{n = 0},\ldots\mspace{14mu},{{QN}_{T} - 1},} & (12)\end{matrix}$while for the remaining antennas m=N_(T)/2+m′, m′=0, 1, . . . ,N_(T)/2−1,

$\begin{matrix}{\begin{matrix}{w_{{{N_{T}/2} + m^{\prime}},n}^{({N_{T},Q})} = {\exp\left( {j\;\frac{2\pi}{N_{T}Q}\left( {{N_{T}/2} + m^{\prime}} \right)n} \right)}} \\{= {{\exp\left( {j\;\frac{2\pi}{\frac{N_{T}}{2}\left( {2\; Q} \right)}m^{\prime}n} \right)}{\exp\left( {j\;\frac{\pi}{Q}n} \right)}}} \\{= {w_{m^{\prime},n}^{({{N_{T}/2},{2Q}})}{\exp\left( {j\;\frac{\pi}{Q}n} \right)}}} \\{{= {w_{m^{\prime},n}^{({{N_{T}/2},{2Q}})}\alpha}},{n = 0},\ldots\mspace{14mu},{{Q\; N_{T}} - 1.}}\end{matrix}{{Here},{\alpha \in {\left\{ {{{{\exp\left( {j\;\frac{\pi}{Q}n} \right)}\text{:}\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{{2Q} - 1}} \right\}.}}}} & (13)\end{matrix}$

Any N_(T) element DFT overall precoder 36 can thus be written as

$\begin{matrix}{w_{n}^{({N_{T},Q})} = {\left\lbrack {w_{0,n}^{({N_{T},Q})}\mspace{14mu} w_{1,n}^{({N_{T},Q})}\mspace{14mu}\ldots\mspace{14mu} w_{{N_{T} - 1},n}^{({N_{T},Q})}\mspace{14mu} w_{0,n}^{({N_{T},Q})}\alpha\mspace{14mu} w_{1,n}^{({N_{T},Q})}\alpha\mspace{14mu}\ldots\mspace{14mu} w_{{N_{T} - 1},n}^{({N_{T},Q})}\alpha} \right\rbrack^{T} = {\quad{\begin{bmatrix}w_{n}^{({{N_{T}/2},{2Q}})} \\{w_{n}^{({{N_{T}/2},{2Q}})}\alpha}\end{bmatrix} = {{\begin{bmatrix}w_{n}^{({{N_{T}/2},{2Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2Q}})}\end{bmatrix}\begin{bmatrix}1 \\\alpha\end{bmatrix}}.}}}}} & (14)\end{matrix}$One sees in the above arrangement that w_(n) ^((N) ^(T) ^(,Q)) may beregarded as an example of an overall precoder 36 formed from aconversion precoder 32 given as

$\begin{bmatrix}w_{n}^{({{N_{T}/2},{2Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2Q}})}\end{bmatrix},$and a tuning precoder 34 given as

$\begin{bmatrix}1 \\\alpha\end{bmatrix}.$Note further that each block, w_(n) ^((N) ^(T) ^(/2,2Q)), of theconversion precoder 32 represents one of the antenna-subgroup precoders38 included in the conversion precoder 32, and note that the tuningprecoders 34 are determined as

$\begin{matrix}{\left\{ {{{\begin{bmatrix}1 \\{\exp\left( {j\;\frac{\pi}{Q}n} \right)}\end{bmatrix}\text{:}\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{{2\; Q} - 1}} \right\}.} & (15)\end{matrix}$

The above arrangement suits the closely spaced cross-polarized antennaarray perfectly because size N_(T)/2 DFT-based antenna-subgroupprecoders 38 are now applied on each antenna group ULA and the tuningprecoder 34 provides 2Q different relative phase shifts between the twoorthogonal polarizations. It is also seen how the N_(T)/2 elementantenna-subgroup precoders 38 are reused for constructing the N_(T)element overall precoder 36. Of further note, the oversampling factor Qis twice as large in the cross-polarized case as it is for theco-polarized case, but those elements are not wasted because they helpto increase the spatial resolution of the grid of beams precoders evenfurther. This characteristic is particularly useful in MU-MIMOapplications where good performance relies on the ability to veryprecisely form beams towards the UE of interest and nulls towards theother co-scheduled UEs.

For example, take a special case of N_(T)=8 transmit antennas—i.e.,assume that the transceiver 10 of FIG. 1 includes eight antennas 14, foruse in precoded MIMO transmissions, and assume that Q=2 for the closelyspaced ULA. One sees that the overall precoder 36 is built up as

$\begin{matrix}\begin{matrix}{w_{n}^{({8,2})} = \begin{bmatrix}w_{n}^{({{N_{T}/2},{2Q}})} \\{w_{n}^{({{N_{T}/2},{2Q}})}\alpha}\end{bmatrix}} \\{{= {\begin{bmatrix}w_{n}^{({4,4})} & 0 \\0 & w_{n}^{({4,4})}\end{bmatrix}\begin{bmatrix}1 \\{\exp\left( {j\;\frac{\pi}{2}n^{\prime}} \right)}\end{bmatrix}}},{n = 0},\ldots\mspace{14mu},{{2\; N_{T}} - 1},} \\{{n^{\prime} = 0},1,2,3.}\end{matrix} & (16)\end{matrix}$The codebook entries for the tuning precoders 34 can then be chosen fromthe rank 1, 2 Tx codebook in LTE and hence that codebook can be re-usedin the teachings disclosed herein. The codebook for the conversionprecoders 32 contains elements constructed from four DFT based generatormatrices as in Eq. (7). The codebook(s) 30 can contain other elements inaddition to the DFT based ones being described here. Broadly, theprinciple of constructing N element DFT-based overall precoders 36 outof smaller, N/2 element DFT-based antenna-subgroup precoders 38 can beused in general to add efficient closely spaced ULA and cross-polesupport to a range of codebook-based precoding schemes. As a furtheradvantage, the disclosed precoder structure can be used even if theantenna setups differ from what is being discussed here.

Further, note that DFT-based overall precoders 36 can be used for highertransmission ranks than one. One way to accomplish this is to pick theconversion precoders 32 as column subsets of DFT-based generatormatrices, such as shown in Eq. (7). The tuning precoders 34 can beextended with additional columns as well, to match the desired value ofthe transmission rank. For transmission rank 2, a tuning precoder 34 canbe structured as

$\begin{matrix}{{W^{(t)} = \begin{bmatrix}1 & 1 \\\alpha & {- \alpha}\end{bmatrix}},{\alpha \in {\left\{ {{{{\exp\left( {j\frac{\pi}{Q}n} \right)}\text{:}\mspace{14mu} n} = 0},1,\ldots\mspace{14mu},{{2\; Q} - 1}} \right\}.}}} & (17)\end{matrix}$

It is sometimes beneficial to re-use existing codebooks in the design ofnew codebooks. However, one associated problem is that existingcodebooks may not contain all the needed DFT precoder vectors to provideat least Q=2 times oversampling of the grid of beams. Assuming forexample that one has an existing codebook for N_(T)/2 antennas with DFTprecoders providing Q=Q_(e) in oversampling factor and that the targetoversampling factor for the N_(T)/2 element antenna group ULA is Q=Q.The spatial resolution of the existing codebook can then be improved tothe target oversampling factor in factorized precoder design as

$\begin{matrix}{{w = {\begin{bmatrix}{\Lambda_{\overset{\sim}{q}}w_{n}^{({{N_{T}/2},Q_{e}})}} & 0 \\0 & {\Lambda_{\overset{\sim}{q}}w_{n}^{({{N_{T}/2},Q_{e}})}}\end{bmatrix}\begin{bmatrix}1 \\\alpha\end{bmatrix}}},{\quad{{n = 0},\ldots\mspace{14mu},{{Q_{e}N_{T}} - 1},{\overset{\sim}{q} = 0},1,\ldots\mspace{14mu},{{{Q_{t}/Q_{e}} - {1\Lambda_{\overset{\sim}{q}}}} = {{{diag}\left( {1,{\exp\left( {j\;\frac{2\pi}{\frac{N_{T}}{2}}\frac{\overset{\sim}{q}}{Q_{t}}1} \right)},{\exp\left( {j\;\frac{2\pi}{\frac{N_{T}}{2}}\frac{\overset{\sim}{q}}{Q_{t}}2} \right)},\ldots\mspace{14mu},{\exp\left( {j\;\frac{2\pi}{\frac{N_{T}}{2}}\frac{\overset{\sim}{q}}{Q_{t}}\left( {{N_{T}/2} - 1} \right)} \right)}} \right)}.}}}}} & (18)\end{matrix}$Here, the w_(n) ^((N) ^(T) ^(/2,Q) ^(e) ⁾ could be elements in theexisting LTE 4 Tx House Holder codebook, which contains 8 DFT basedprecoders (using an oversampling factor of Q=2 so that there is someoverlap among the beams spanning four antennas) for rank 1. When thetransmission rank is higher than one, the block diagonal structure canbe maintained and the structure thus generalizes to

$\begin{matrix}{{W = {\begin{bmatrix}{\Lambda_{\overset{\sim}{q}}{\overset{\sim}{W}}^{(c)}} & 0 \\0 & {\Lambda_{\overset{\sim}{q}}{\overset{\sim}{W}}^{(c)}}\end{bmatrix}W^{(t)}}},} & (19)\end{matrix}$where W is now an N_(T)×r matrix, {tilde over (W)}^((c)) is a matrixwith at least one column equal to a DFT based antenna-subgroup precoderw_(n) ^((N) ^(T) ^(/2,Q) ^(e) ⁾, and the tuning precoder W^((t)) has rcolumns.

To see that that the spatial resolution can be improved by multiplyingan antenna-subgroup precoder 38 with a diagonal matrix as describedabove, consider the alternative parameterization of DFT precoders in Eq.(6),

$\begin{matrix}{{w_{m,{{Q_{t}l} + q}}^{({N_{T},Q_{t}})} = {\exp\left( {j\;\frac{2\pi}{N_{T}}{m\left( {l + \frac{q}{Q_{t}}} \right)}} \right)}},{m = 0},\ldots\mspace{14mu},{N_{T} - 1},{l = 0},\ldots\mspace{14mu},{N_{T} - 1},{q = 0},\ldots\mspace{14mu},{Q_{t} - 1},} & (20)\end{matrix}$and let

$\begin{matrix}{{q = {{\frac{Q_{t}}{Q_{e}}q^{\prime}} + \overset{\sim}{q}}},{q^{\prime} = 0},\ldots\mspace{14mu},{Q_{e} - 1},{\overset{\sim}{q} = 0},\ldots\mspace{14mu},{\frac{Q_{t}}{Q_{e}} - 1},} & (21)\end{matrix}$to arrive at

$\begin{matrix}{\begin{matrix}{\mspace{79mu}{w_{m,{{Q_{t}l} + {\frac{Q_{t}}{Q_{e}}q^{\prime}} + \overset{\sim}{q}}}^{({N_{T},Q_{t}})} = {\exp\left( {j\;\frac{2\pi}{N_{T}}{m\left( {l + {\frac{1}{Q_{t}}\left( {{\frac{Q_{t}}{Q_{e}}q^{\prime}} + \overset{\sim}{q}} \right)}} \right)}} \right)}}} \\{= {{\exp\left( {j\;\frac{2\pi}{N_{T}}{m\left( {l + \frac{q^{\prime}}{Q_{e}}} \right)}} \right)}{\exp\left( {j\;\frac{2\pi}{N_{T}}m\;\frac{\overset{\sim}{q}}{Q_{t}}} \right)}}} \\{= {w_{m,{{Q_{e}l} + q^{\prime}}}^{({N_{T},Q_{e}})}{\exp\left( {j\;\frac{2\pi}{N_{T}}m\;\frac{\overset{\sim}{q}}{Q_{t}}} \right)}}}\end{matrix}{{{{for}\mspace{14mu} m} = 0},\ldots\mspace{14mu},{N_{T} - 1},{l = 0},\ldots\mspace{14mu},{N_{T} - 1},{q^{\prime} = 0},\ldots\mspace{14mu},{Q_{e} - 1},{\overset{\sim}{q} = 0},\ldots\mspace{14mu},{\frac{Q_{t}}{Q_{e}} - 1.}}} & (22)\end{matrix}$

The above formulations demonstrate an advantageous aspect of theteachings presented herein. Namely, a codebook containing DFT precoderswith oversampling factor Q_(e) can be used for creating a higherresolution DFT codebook by multiplying the m:th element with

$\exp\left( {j\;\frac{2\pi}{N_{T}}m\;\frac{\overset{\sim}{q}}{Q_{t}}} \right)$and hence proving that the diagonal transformation given byΛ_({tilde over (q)}) indeed works as intended.

Another issue to take into account when designing precoders is to ensurean efficient use of the power amplifiers (PAs), e.g., the PAs in thetransmitters 18 used for multi-antenna transmission from the transceiver10. Usually, power cannot be borrowed across antennas because there is aseparate PA for each antenna. Hence, for maximum use of the PAresources, it is important that the same amount of power is transmittedfrom each antenna. In other words, an overall precoder matrix W forprecoding from the transmit antennas should fulfill[WW*] _(mm) =κ,∇m.  (23)

Thus, it is beneficial from a PA utilization point of view to enforcethis constraint when designing precoder codebooks. Full powerutilization is also ensured by the so-called constant modulus property,which means that all scalar elements in a precoder have the same norm(modulus). It is easily verified that a constant modulus precoder alsofulfills the full PA utilization constraint in Eq. (23). Hence, theconstant modulus property constitutes a sufficient but not necessarycondition for full PA utilization.

With the beneficial aspect of full PA utilization in mind, anotheraspect of the teachings presented herein relates to providing precodersthat yield full PA utilization. In particular, one or more embodimentsproposed herein solve the problems associated with full PA utilizationand satisfaction of the rank nested property, in the context of afactorized precoder design. By using a so-called double block diagonaltuning precoder 34 combined with a block diagonal conversion precoder32, full PA utilization is guaranteed and rank override exploiting thenested property is also possible for the overall precoder formed as thecombination of a conversion precoder 32 and a tuning precoder 34 havingthe properties and structure disclosed herein.

A first step in designing efficient factorized precoder codebooks whileachieving full PA utilization and fulfilling rank nested property is tomake the conversion precoders block diagonal as shown in Eq. (3), forexample. In a particular case, the number of columns k of a conversionprecoder is made equal to 2┌r/2┐, where ┌·┐ denotes the ceil function.This structure is achieved by adding two new columns contributingequally much to each polarization for every other rank. In other words,the conversion precoder 32 at issue here can be denoted as W^((c)) andwritten in the form

$\begin{matrix}{W^{(c)} = {\begin{bmatrix}{\overset{\sim}{W}}^{(c)} & 0 \\0 & {\overset{\sim}{W}}^{(c)}\end{bmatrix} = {\quad{\begin{bmatrix}{\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)} & 0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 & {\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)}\end{bmatrix},}}}} & (24)\end{matrix}$where {tilde over (w)}_(l) ^((c)) is an N_(T)/2×1 vector.

Extending the conversion dimension in this manner helps keep the numberof dimensions small and in addition serves to make sure that bothpolarizations are excited equally much. It is beneficial if theconversion precoder, denoted here as {tilde over (W)}^((c)), is alsomade to obey a generalized rank nested property in that there is freedomto choose {tilde over (W)}^((c)) with L columns as an arbitrary columnsubset of each possible {tilde over (W)}^((c)) with L+1 columns. Analternative is to have the possibility to signal the column orderingused in {tilde over (W)}^((c)). Flexibility in the choice of columns for{tilde over (W)}^((c)) for the different ranks is beneficial so as tostill be able to transmit into the strongest subspace of the channeleven when rank override using a column subset is performed.

Further, as regards to ensuring full PA utilization, e.g., at thetransceiver 10, the tuning precoders 34, which are denoted as W^((t)),are in one or more embodiments constructed as follows: (a) theconversion vector {tilde over (w)}_(n) ^((c)) is made constant modulus;and (b) a column in the tuning precoder has exactly two non-zeroelements with constant modulus. If the m:th element is non-zero, so iselement m+┌r/2┐. Hence for rank r=4, the columns in the tuning precoder34 are of the following form

$\begin{matrix}{\begin{bmatrix}x \\0 \\x \\0\end{bmatrix},\begin{bmatrix}0 \\x \\0 \\x\end{bmatrix},} & (25)\end{matrix}$where x denotes an arbitrary non-zero value which is not necessarily thesame from one x to another. Because there are two non-zero elements in acolumn, two orthogonal columns with the same positions of the non-zeroelements can be added before columns with other non-zero positions areconsidered. Such pairwise orthogonal columns with constant modulusproperty can be parameterized as

$\begin{matrix}{\begin{bmatrix}1 \\0 \\{\mathbb{e}}^{j\phi} \\0\end{bmatrix},{\begin{bmatrix}1 \\0 \\{- {\mathbb{e}}^{j\phi}} \\0\end{bmatrix}.}} & (26)\end{matrix}$Rank nested property for the overall precoder is upheld when increasingthe rank by one by ensuring that columns for previous ranks excite thesame columns of the conversion precoder also for the higher rank.Combining this with Eq. (25) and the mentioned pairwise orthogonalproperty of the columns leads to a double block diagonal structure ofthe tuning precoder taking the form

$\begin{matrix}{W = {\begin{bmatrix}{\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)} & 0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 & {\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)}\end{bmatrix}{\quad{\begin{bmatrix}x & x & 0 & 0 & \ldots & \; & \; & \; \\0 & 0 & x & x & \; & \; & \; & \; \\\vdots & \; & \; & \; & \ddots & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; \\x & x & 0 & 0 & \ldots & \; & \; & \; \\0 & 0 & x & x & \; & \; & \; & \; \\\vdots & \; & \; & \; & \ddots & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \;\end{bmatrix}.}}}} & (27)\end{matrix}$Using the pairwise orthogonality property in Eq. (26), and representingthe structure for the overall precoder 36, denoted as W, asW=W^((c))W^((t)), the precoder structure can be further specialized into

$\begin{matrix}{W = {\begin{bmatrix}{\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)} & 0 & 0 & \ldots & 0 \\0 & 0 & \ldots & 0 & {\overset{\sim}{w}}_{1}^{(c)} & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)}\end{bmatrix}{\quad{\begin{bmatrix}1 & 1 & 0 & 0 & \ldots & \; & \; & \; \\0 & 0 & 1 & 1 & \; & \; & \; & \; \\\vdots & \; & \; & \; & \ddots & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \; \\{\mathbb{e}}^{j\;\phi_{1}} & {- {\mathbb{e}}^{j\;\phi_{1}}} & 0 & 0 & \ldots & \; & \; & \; \\0 & 0 & {\mathbb{e}}^{j\;\phi_{2}} & {- {\mathbb{e}}^{j\;\phi_{2}}} & \; & \; & \; & \; \\\vdots & \; & \; & \; & \ddots & \; & \; & \; \\\; & \; & \; & \; & \; & \; & \; & \;\end{bmatrix}.}}}} & (28)\end{matrix}$Note that the double block diagonal structure for the tuning precodercan be described in different ways depending on the ordering of thecolumns used for storing the conversion precoders W^((c)) as entries inthe codebook 26. It is possible to equivalently make the tuningprecoders W^((t)) block diagonal by writing

$\begin{matrix}{W = {\begin{bmatrix}{\overset{\sim}{w}}_{1}^{(c)} & 0 & {\overset{\sim}{w}}_{2}^{(c)} & 0 & \ldots & \ldots & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)} & 0 \\0 & {\overset{\sim}{w}}_{1}^{(c)} & 0 & {\overset{\sim}{w}}_{2}^{(c)} & \ldots & \ldots & 0 & {\overset{\sim}{w}}_{\lceil{r/2}\rceil}^{(c)}\end{bmatrix}{\quad{\begin{bmatrix}x & x & 0 & 0 & \ldots & \; & 0 & 0 \\x & x & 0 & 0 & \; & \; & \; & \vdots \\0 & 0 & x & x & \ddots & \; & \; & \; \\\vdots & \; & x & x & \; & \; & \; & \; \\\; & \; & 0 & 0 & \ddots & \; & \; & \; \\\; & \; & \vdots & \; & \; & \; & 0 & 0 \\\vdots & \; & \; & \; & \ddots & \; & x & x \\0 & 0 & 0 & 0 & \ldots & 0 & x & x\end{bmatrix}.}}}} & (29)\end{matrix}$Re-orderings similar to these do not affect the overall precoder W andare thus considered equivalent and assumed to be covered under the terms“block diagonal conversion precoder and double block diagonal tuningprecoder.” It is also interesting to note that if the requirements onthe orthogonality constraint and full PA utilization are relaxed, thedesign for rank nested property can be summarized with the followingstructure for the tuning precoders 34

$\begin{matrix}{\quad{\begin{bmatrix}x & x & x & x & x & x & \; & \; \\0 & 0 & x & x & x & x & \; & \; \\\vdots & \; & \; & \; & x & x & \ddots & \; \\\; & \; & \; & \; & \; & \; & \; & \; \\{x\;} & {x\;} & x & x & x & x & \; & \; \\0 & 0 & x & x & x & x & \; & \; \\\vdots & \; & \; & \; & x & x & \ddots & \; \\\; & \; & \; & \; & \; & \; & \; & \;\end{bmatrix}.}} & (30)\end{matrix}$

Further, it is worth mentioning that rank nested property can be usefulwhen applied separately to the conversion precoders 32 and the tuningprecoders 34. Even applying it only to the tuning precoders 34 can helpsave computational complexity, because precoder calculations acrossranks can be re-used as long as the selected conversion precoder W^((c))remains fixed.

As an illustrative example for eight transmit antennas 14 at thetransceiver 10, assume that Rank r=1

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & \; \\\; & w_{1}^{(1)}\end{bmatrix}\begin{bmatrix}1 \\{\mathbb{e}}^{j\;\varphi_{k}}\end{bmatrix}}} & (31)\end{matrix}$Rank r=2

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & \; \\\; & w_{1}^{(1)}\end{bmatrix}\begin{bmatrix}1 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}}\end{bmatrix}}} & (32)\end{matrix}$Rank r=3

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & \; & \; \\\; & \; & w_{1}^{(1)} & w_{2}^{(1)}\end{bmatrix}\begin{bmatrix}1 & 1 & 0 \\0 & 0 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {\mathbb{e}}^{j\;\varphi_{k}} & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}}\end{bmatrix}}} & (33)\end{matrix}$Rank r=4

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & \; & \; \\\; & \; & w_{1}^{(1)} & w_{2}^{(1)}\end{bmatrix}\begin{bmatrix}1 & 1 & 0 & 0 \\0 & 0 & 1 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}} & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}} & {- {\mathbb{e}}^{j\;\varphi_{l}}}\end{bmatrix}}} & (34)\end{matrix}$Rank r=5

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & \; & \; & \; \\\; & \; & \; & w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)}\end{bmatrix}\left\lbrack \begin{matrix}1 & 1 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}} & 0 & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}} & {- {\mathbb{e}}^{j\;\varphi_{l}}} & 0 \\0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{m}}\end{matrix} \right\rbrack}} & (35)\end{matrix}$Rank r=6

$\begin{matrix}{W = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & \; & \; & \; \\\; & \; & \; & w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)}\end{bmatrix}\left\lbrack \begin{matrix}1 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}} & 0 & 0 & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}} & {- {\mathbb{e}}^{j\;\varphi_{l}}} & 0 & 0 \\0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{m}} & {- {\mathbb{e}}^{j\;\varphi_{m}}}\end{matrix} \right\rbrack}} & (36)\end{matrix}$Rank r=7

$\begin{matrix}{w = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & w_{4}^{(1)} & \; & \; & \; & \; \\\; & \; & \; & \; & w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & w_{4}^{(1)}\end{bmatrix}\left\lbrack \begin{matrix}1 & 1 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 1 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}} & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}} & {- {\mathbb{e}}^{j\;\varphi_{l}}} & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{m}} & {- {\mathbb{e}}^{j\;\varphi_{m}}} & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{n}}\end{matrix} \right\rbrack}} & (37)\end{matrix}$Rank r=8

$\begin{matrix}{w = {\begin{bmatrix}w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & w_{4}^{(1)} & \; & \; & \; & \; \\\; & \; & \; & \; & w_{1}^{(1)} & w_{2}^{(1)} & w_{3}^{(1)} & w_{4}^{(1)}\end{bmatrix}\left\lbrack \begin{matrix}1 & 1 & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & 1 & 1 & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & 1 & 1 & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \\{\mathbb{e}}^{j\;\varphi_{k}} & {- {\mathbb{e}}^{j\;\varphi_{k}}} & 0 & 0 & 0 & 0 & 0 & 0 \\0 & 0 & {\mathbb{e}}^{j\;\varphi_{l}} & {- {\mathbb{e}}^{j\;\varphi_{l}}} & 0 & 0 & 0 & 0 \\0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{m}} & {- {\mathbb{e}}^{j\;\varphi_{m}}} & 0 & 0 \\0 & 0 & 0 & 0 & 0 & 0 & {\mathbb{e}}^{j\;\varphi_{n}} & {- {\mathbb{e}}^{j\;\varphi_{n}}}\end{matrix} \right\rbrack}} & (38)\end{matrix}$The 4 Tx case follows in a similar manner.

With the above in mind, the following structure and provisions areproposed herein, for one or more embodiments that provide for full PAutilization:

-   -   1. The overall precoder 36 can be factorized into a conversion        precoder 32 and a tuning precoder 34.        -   a. the conversion precoder 32 is block diagonal        -   b. the tuning precoder 36 has the properties:            -   i. all non-zero elements are constant modulus            -   ii. every column has exactly two non-zero elements            -   iii. every row has exactly two non-zero elements    -   2. Two columns in the tuning precoder 34 either have non-zero        elements in the same two rows or do not have any non-zero        elements in the same rows.    -   3. Two columns in the tuning precoder 34 having non-zero        elements in the same two rows are orthogonal to each other.    -   4. The conversion precoder 32 has 2┌k/2┐ columns and if row m in        a tuning precoder column has a non-zero element, so does row        m+┌k/2┐.    -   5. The columns of the tuning precoder 34 for rank r is a subset        of the columns of the tuning precoder for rank r+1

With the above in mind, one method herein comprises a method ofprecoding multi-antenna transmissions 60 from a wireless communicationtransceiver 10 to another wireless communication transceiver 12. Themethod includes selecting an overall precoder 36, determiningtransmission weights for respective ones of two or more transmitantennas 14 according to the selected overall precoder 36, andtransmitting weighted signals from the two or more transmit antennas 14in accordance with the transmission weights. The selected precoder isselected at least in part based on considering precoder informationreceived from the second transceiver 12, which includes indications ofprecoder selections made by the second transceiver 12, which areintended as precoding recommendations to be considered by the firsttransceiver 10.

According to the above method, the overall precoder 36 factorizes into aconversion precoder 32 and a tuning precoder 34, wherein the conversionprecoder 32 is block diagonal and wherein the tuning precoder 34 has thefollowing properties: all non-zero elements are constant modulus; everycolumn has exactly two non-zero elements; and every row has exactly twonon-zero elements; two columns either have non-zero elements in the sametwo rows or do not have any non-zero elements in the same rows; and twocolumns having non-zero elements in the same two rows are orthogonal toeach other. Further, the conversion precoder 32 has 2┌k/2┐ columns,where k is a non-negative integer, and if row m in a tuning precodercolumn has a non-zero element, so does row m+┌k/2┐.

Further, in at least one such embodiment, the columns of a tuningprecoder 34 for rank r is a subset of the columns of a tuning precoderfor rank r+1.

Similarly, another method disclosed herein provides for sendingprecoding information from a second transceiver 12 to a firsttransceiver 10 that considers the precoding information in selectingprecoders for precoding multi-antenna transmissions 60 to the secondtransceiver 12.

The method includes the second transceiver 12 selecting an overallprecoder 36 that factorizes into a conversion precoder 32 and a tuningprecoder 34, or selecting the conversion precoder 32 and the tuningprecoder 34 corresponding to a particular overall precoder 36, andsending to the first transceiver 10 as said precoder information anindication of the selected overall precoder 36 or indications of theselected conversion and tuning precoders 32, 34.

For this method, the conversion precoders 32 are each block diagonal andeach tuning precoder 34 has the following properties: all non-zeroelements are constant modulus; every column has exactly two non-zeroelements; and every row has exactly two non-zero elements; two columnseither have non-zero elements in the same two rows or do not have anynon-zero elements in the same rows; and two columns having non-zeroelements in the same two rows are orthogonal to each other.Additionally, according to the method, the conversion precoder 32 has2┌k/2┐ columns, where k is a non-negative integer, and if row m in atuning precoder column has a non-zero element, so does row m+┌k/2┐.Still further, in at least one embodiment, the columns of a tuningprecoder 34 for rank r is a subset of the columns of a tuning precoderfor rank r+1.

Of course, the teachings herein are not limited to the specific,foregoing illustrations. For example, terminology from 3GPP LTE was usedin this disclosure to provide a relevant and advantageous context forunderstanding operations at the transceivers 10 and 12, which wereidentified in one or more embodiments as being an LTE eNodeB and an LTEUE, respectively. However, the teachings disclosed herein are notlimited to these example illustrations and may be advantageously appliedto other contexts, such as networks based on WCDMA, WiMax, UMB or GSM.

Further, the transceiver 10 and the transceiver 12 are not necessarily abase station and an item of mobile equipment within a standard cellularnetwork, although the teachings herein have advantages in such acontext. Moreover, while certain wireless network examples given hereininvolve the “downlink” from an eNodeB or other network base station, theteachings presented herein also have applicability to the uplink. Morebroadly, it will be understood that the teachings herein are limited bythe claims and their legal equivalents, rather than by the illustrativeexamples given herein.

What is claimed is:
 1. A wireless communication transceiver configuredto send channel state information to another wireless communicationtransceiver that precodes transmissions to the transceiver based atleast in part on the channel state information, said transceiverincluding a receiver for receiving signals from the other transceiverand a transmitter for transmitting signals to the other transceiver,including transmitting signals conveying said channel state information,wherein said transceiver comprises: a memory storing one or morecodebooks including entries comprising a plurality of differentconversion precoders and entries comprising a number of correspondingtuning precoders, or entries comprising a plurality of overallprecoders, with each overall precoder comprising a product of one of theplurality of different conversion precoders and one of the number ofcorresponding tuning precoders; wherein each said conversion precodercomprises a block diagonal matrix; wherein each tuning precoder has thefollowing properties: all non-zero elements are constant modulus; everycolumn has exactly two non-zero elements; every row has exactly twonon-zero elements; two columns either have non-zero elements in the sametwo rows or do not have any non-zero elements in the same rows; and twocolumns having non-zero elements in the same two rows are orthogonal toeach other; and further wherein the conversion precoder has 2┌k/2┐columns, where k is a non-negative integer, and if row m in the tuningprecoder column has a non-zero element, so does row m+┌k/2┐; andprocessing circuits configured to: select entries from the one or morecodebooks as a selected conversion precoder and a selected tuningprecoder, or as a selected overall precoder corresponding to theselected conversion precoder and the selected tuning precoder; andtransmit, via said transmitter, indications of the selected entries asprecoder information included in said channel state information.
 2. Thetransceiver according to claim 1 wherein the columns of the tuningprecoder for rank r is a subset of the columns of the tuning precoderfor rank r+1.
 3. A wireless communication transceiver configured toprecode multi-antenna transmissions to another wireless communicationtransceiver based at least in part on receiving channel stateinformation from the other transceiver, said transceiver including atransmitter and a plurality of antennas for transmitting saidmulti-antenna transmissions and a receiver for receiving the channelstate information, and wherein the transceiver comprises: a memorystoring one or more codebooks including entries comprising a pluralityof different conversion precoders and entries comprising a number ofcorresponding tuning precoders, or entries comprising a plurality ofoverall precoders, with each overall precoder comprising a product ofone of the plurality of different conversion precoders and one of thenumber of corresponding tuning precoders; wherein each said conversionprecoder comprises a block diagonal matrix; wherein each tuning precoderhas the following properties: all non-zero elements are constantmodulus; every column has exactly two non-zero elements; every row hasexactly two non-zero elements; two columns either have non-zero elementsin the same two rows or do not have any non-zero elements in the samerows; and two columns having non-zero elements in the same two rows areorthogonal to each other; and further wherein the conversion precoderhas 2┌k/2┐ columns, where k is a non-negative integer, and if row m inthe tuning precoder column has a non-zero element, so does row m+┌k/2┐;processing circuits configured to select an overall precoder; anddetermine transmission weights for respective ones of two or moretransmit antennas based at least in part on the selected overallprecoder; and wherein the transmitter is configured to transmit weightedsignals from the two or more transmit antennas in accordance with thetransmission weights.
 4. The transceiver according to claim 3 whereinthe columns of the tuning precoder for rank r is a subset of the columnsof the tuning precoder for rank r+1.
 5. A wireless communicationtransceiver configured to send channel state information to anotherwireless communication transceiver that precodes transmissions to thetransceiver based at least in part on the channel state information,said transceiver including a receiver for receiving signals from theother transceiver and a transmitter for transmitting signals to theother transceiver, including transmitting signals conveying said channelstate information, wherein said transceiver comprises: a memory storingone or more codebooks including entries comprising N_(T)Q differentconversion precoders and entries comprising a number of correspondingtuning precoders, or entries comprising a plurality of overallprecoders, with each overall precoder comprising a product of one of theN_(T)Q different conversion precoders and one of the number ofcorresponding tuning precoders; wherein each said conversion precoderout of said N_(T)Q different entries comprises a block diagonal matrixin which each block comprises a discrete Fourier transform (DFT)-basedantenna-subgroup precoder that corresponds to a subgroup of N_(T)transmit antenna ports and provides N_(T)Q different DFT based beams forthe corresponding subgroup, where Q is an integer value and where theN_(T)Q different conversion precoders, together with one or more of thetuning precoders, correspond to a set of N_(T)Q different overallprecoders; and wherein each overall precoder represents a size-N_(T)DFT-based beam over the N_(T) transmit antennas ports; and processingcircuits configured to: select entries from the one or more codebooks asa selected conversion precoder and a selected tuning precoder, or as aselected overall precoder corresponding to the selected conversionprecoder and the selected tuning precoder; and transmit, via saidtransmitter, indications of the selected entries as precoder informationincluded in said channel state information.
 6. The transceiver of claim5, wherein the other transceiver is a base station in a wirelesscommunication network and the transceiver is a user equipment, UE,sending said channel state information to said base station.
 7. Thetransceiver of claim 6, wherein said base station and said UE maintaincopies of the same one or more codebooks, and wherein said UE transmitsthe indications of the selected entries as said precoder information bytransmitting index values to the base station that indicate the selectedentries in the one or more codebooks.
 8. The transceiver of claim 5,wherein said each antenna-subgroup precoder is a matrix block withN_(T)/2 rows and belongs to a set of N_(T)Q different DFT-based beams,where Q is an integer equal to or greater than 2, and where each saidtuning precoder includes a phase shift element taken from a 2Q PhaseShift Keying (PSK) alphabet and provides at least 2Q relative phaseshifts for offsetting beam phases between the antenna-subgroup precodersin a corresponding one of the conversion precoders.
 9. The transceiverof claim 5, wherein the transceiver is configured to transmit theindications of the selected entries as said precoder information bytransmitting conversion precoder selections according to a first time orfrequency resolution and transmitting tuning precoder selectionsaccording to a second time or frequency resolution that is higher thansaid first time or frequency resolution.
 10. The transceiver of 5,wherein said one or more codebooks include conversion and tuningprecoders for two or more transmission ranks, or corresponding overallprecoders for two or more transmission ranks.
 11. The transceiver ofclaim 5, wherein each conversion precoder can be written in the form$\begin{bmatrix}w_{n}^{({{N_{T}/2},{2\; Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2\; Q}})}\end{bmatrix},$ where ${w_{n}^{({N_{T},Q})} = \begin{bmatrix}w_{1,n}^{({N_{T},Q})} & w_{2,n}^{({N_{T},Q})} & \ldots & w_{N_{T},n}^{({N_{T},Q})}\end{bmatrix}^{T}},{and}$${w_{m,n}^{({N_{T},Q})} = {\exp\left( {j\frac{2\;\pi}{N_{T}Q}{mn}} \right)}},{m = 0},\ldots\mspace{14mu},{N_{T} - 1},{n = 0},\ldots\mspace{14mu},{{QN}_{T} - 1},$where w_(m,n) ^((N) ^(T) ^(,Q)) is the phase of the m:th antenna port, nis a precoder vector index indicating one of the N_(T)Q beams and Qrepresents an oversampling factor, and where each tuning precoder (34)can be written in the form $\begin{bmatrix}1 \\\alpha\end{bmatrix},$ where ${\alpha \in \left\{ {{{\begin{bmatrix}1 \\{\exp\left( {j\frac{\pi}{Q}n} \right)}\end{bmatrix}\text{:}\mspace{25mu} n} = 0},1,\ldots\mspace{14mu},{{2\; Q} - 1}} \right\}},$and where the corresponding overall precoder can be written in the form${\begin{bmatrix}w_{n}^{({{N_{T}/2},{2\; Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2\; Q}})}\end{bmatrix}\begin{bmatrix}1 \\\alpha\end{bmatrix}}.$
 12. A wireless communication transceiver configured toprecode multi-antenna transmissions to another wireless communicationtransceiver based at least in part on receiving channel stateinformation from the other transceiver, said transceiver including atransmitter and a plurality of antennas for transmitting saidmulti-antenna transmissions and a receiver for receiving the channelstate information, and wherein the transceiver comprises: a memorystoring one or more codebooks including entries comprising N_(T)Qdifferent conversion precoders and entries comprising a number ofcorresponding tuning precoders, or entries comprising a plurality ofoverall precoders, with each overall precoder comprising a product ofone of the N_(T)Q different conversion precoders and one of the numberof corresponding tuning precoders; wherein each said conversion precoderout of said N_(T)Q different entries comprises a block diagonal matrixin which each block comprises a discrete Fourier transform (DFT)-basedantenna-subgroup precoder that corresponds to a subgroup of N_(T)transmit antenna ports and provides N_(T)Q different DFT based beams forthe corresponding subgroup, where Q is an integer value, and where theN_(T)Q different conversion precoders together with one or more of thetuning precoders correspond to a set of N_(T)Q different overallprecoders; and wherein each overall precoder represents a size-N_(T)DFT-based beam over the N_(T) transmit antenna ports; and processingcircuits configured to: identify precoder information from the othertransceiver based on using selection indications included in the channelstate information to identify from the one or more codebooks a selectedconversion precoder and a tuning precoder, or a selected overallprecoder corresponding to the selected conversion precoder and thetuning precoder; and precode the transmission to the other transceiver,based at least in part on the precoder information.
 13. The transceiverof claim 12, wherein the processing circuits are configured to precodethe transmission to the other transceiver by performing DFT-basedprecoding of transmissions from two or more subgroups of the antennasusing antenna-subgroup precoders in the conversion or overall precoderselected by the transceiver from the one or more codebooks, where saidselection by the transceiver is based at least in part on the precoderinformation received from the other transceiver.
 14. The transceiver ofclaim 13, wherein each antenna-subgroup precoder is a matrix block withN_(T)/2 rows and belongs to a set of N_(T)Q different DFT-based beams,where Q is an integer equal to or greater than 2, and where each saidtuning precoder includes a phase shift element taken from a 2Q PhaseShift Keying (PSK) alphabet and provides at least 2Q relative phaseshifts for offsetting beam phases between the antenna-subgroup precodersin a corresponding one of the conversion precoders.
 15. The transceiverof claim 12, wherein the processing circuits are configured to receivesaid selection indications in said channel state information as firstindications received at first time or frequency resolution and secondindications at a second time or frequency resolution higher than saidfirst time or frequency resolution, wherein said first indicationsindicate the selected conversion precoder and said second indicationsindicate the selected tuning precoder.
 16. The transceiver of claim 12,wherein the processing circuits are configured to determine two or moreselected overall precoders, based on said selection indications from theother transceiver including an indication of the selected conversionprecoder and indications of two or more correspondingly selected tuningprecoders, each of which corresponds to a different frequency sub-bandof an overall frequency band associated with the selected conversionprecoder.
 17. The transceiver of claim 12, wherein the processingcircuits are configured to maintain two or more updated overallprecoders based on a commonly selected conversion precoder and two moredifferent, frequency-selective tuning precoders, selected for sub-bandsof a wider frequency spectrum corresponding to the commonly selectedconversion precoder.
 18. The transceiver of claim 12, wherein eachconversion precoder can be written in the form $\begin{bmatrix}w_{n}^{({{N_{T}/2},{2\; Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2\; Q}})}\end{bmatrix},$ where ${w_{n}^{({N_{T},Q})} = \begin{bmatrix}w_{1,n}^{({N_{T},Q})} & w_{2,n}^{({N_{T},Q})} & \ldots & w_{N_{T},n}^{({N_{T},Q})}\end{bmatrix}^{T}},{and}$${w_{m,n}^{({N_{T},Q})} = {\exp\left( {j\frac{2\;\pi}{N_{T}Q}{mn}} \right)}},{m = 0},\ldots\mspace{14mu},{N_{T} - 1},{n = 0},\ldots\mspace{14mu},{{QN}_{T} - 1},$where w_(m,n) ^((N) ^(T) ^(,Q)) is the phase of the m:th antenna port, nis a precoder vector index indicating one of the N_(T)Q beams and Qrepresents an oversampling factor, and where each tuning precoder can bewritten in the form $\begin{bmatrix}1 \\\alpha\end{bmatrix},$ where ${\alpha \in \left\{ {{{\begin{bmatrix}1 \\{\exp\left( {j\frac{\pi}{Q}n} \right)}\end{bmatrix}\text{:}\mspace{25mu} n} = 0},1,\ldots\mspace{14mu},{{2\; Q} - 1}} \right\}},$and where the corresponding overall precoder can be written in the form${\begin{bmatrix}w_{n}^{({{N_{T}/2},{2\; Q}})} & 0 \\0 & w_{n}^{({{N_{T}/2},{2\; Q}})}\end{bmatrix}\begin{bmatrix}1 \\\alpha\end{bmatrix}}.$